There are some clear drawbacks with just about every candidate. While Low appears to be a frontrunner, he will be busy for much of the summer as Germany looks to defend its World Cup title in Russia. Arsenal would probably want a manager to begin the campaign immediately and with a firm understanding of the roster as well as the transfer market.

Jardim might seem like an obvious choice. The 43-year-old has 20 years of managerial experience and is reportedly interested in leaving AS Monaco. But he has bounced around several teams and leagues, and boasts just a 56 percent winning percentage with Monaco in four seasons.

Allegri has done an exceptional job with Juventus and is considered among the most coveted managers in European football. However, Arsenal might want to avoid pursuing Allegri if the rumors are accurate that he could end up at Chelsea. It wouldn't look good if Arsenal pursued Allegri only to see him spurn them for a London rival. Arsenal also would almost certainly pay a hefty price to land the 50-year-old Italian.

Gazidis has hinted that Arsenal may not make the "safe choice" to replace Wenger.

"I think we've got to be open-minded and also brave in the decision. When Arsene was appointed, I don't think he was on many people's radar screens," Gazidis said. "Now that doesn't mean we have to make another appointment that not everybody is thinking about and talking about. But it does mean we need to be bold in the appointment and get the person that we believe is the right person."

Arsene Wenger is stepping down after 22 years with Arsenal.Photo: Julian Finney/Getty Images